Yes, paint will run under the tape unless it is well sealed as der_jackal mentioned. Silly Putty might work, but it tends to flow and unless you spray quick your masking might change over time.
You might try some of the liquid masking fluid. Some people have reported good luck wiith it, I haven't had much of that.
If it were me, I'd use Tamiya masking tape (because it is so thin) and work it down into the creases very well. If the paint bleeds a little, use the first color to touch things up.